Solve for $y$, $ -\dfrac{9}{9y^2} = -\dfrac{5y - 4}{9y^2} - \dfrac{7}{3y^2} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $9y^2$ $9y^2$ and $3y^2$ The common denominator is $9y^2$ The denominator of the first term is already $9y^2$ , so we don't need to change it. The denominator of the second term is already $9y^2$ , so we don't need to change it. To get $9y^2$ in the denominator of the third term, multiply it by $\frac{3}{3}$ $ -\dfrac{7}{3y^2} \times \dfrac{3}{3} = -\dfrac{21}{9y^2} $ This give us: $ -\dfrac{9}{9y^2} = -\dfrac{5y - 4}{9y^2} - \dfrac{21}{9y^2} $ If we multiply both sides of the equation by $9y^2$ , we get: $ -9 = -5y + 4 - 21$ $ -9 = -5y - 17$ $ 8 = -5y $ $ y = -\dfrac{8}{5}$